A Power Differentiation Method of Fractal Dimension Estimation for 2-D Signals

Asvestas, Pantelis A.; Matsopoulos, G. K.; Nikita, Konstantina S.

doi:10.1006/jvci.1998.0394

Cited by 40 publications

(16 citation statements)

References 21 publications

(19 reference statements)

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“…Analysis with the application of D dimension to the examination of differently machined profiles presented in Figs. [8][9][10][11] shows that the most complex profiles were obtained using carbon nanotube nanofluids with pulse current 5 A, pulse duration 3 µs, pulse voltage 80 V, D = 1.424. On the other hand, the lowest D values were reached after machining with carbon nanotube nanofluids with pulse current 8 A, pulse duration 1 µs, pulse voltage 100 V, D = 0.9106.…”

Section: Fractal Analysismentioning

confidence: 99%

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Multiresponse Optimization of Edm Process with Nanofluids Using Topsis Method and Genetic Algorithm

Prabhu¹,

Vinayagam²

2016

Archive of Mechanical Engineering

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Electrical Discharge Machining (EDM) process with copper tool electrode is used to investigate the machining characteristics of AISI D2 tool steel material. The multi-wall carbon nanotube is mixed with dielectric fluids and its end characteristics like surface roughness, fractal dimension and metal removal rate (MRR) are analysed. In this EDM process, regression model is developed to predict surface roughness. The collection of experimental data is by using L9 Orthogonal Array. This study investigates the optimization of EDM machining parameters for AISI D2 Tool steel using Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method. Analysis of variance (ANOVA) and F-test are used to check the validity of the regression model and to determine the significant parameter affecting the surface roughness. Atomic Force Microscope (AFM) is used to capture the machined image at micro size and using spectroscopy software the surface roughness and fractal dimensions are analysed. Later, the parameters are optimized using MINITAB 15 software, and regression equation is compared with the actual measurements of machining process parameters. The developed mathematical model is further coupled with Genetic Algorithm (GA) to determine the optimum conditions leading to the minimum surface roughness value of the workpiece.

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Section: Fractal Analysismentioning

confidence: 99%

“…The surface characteristics of this lead zirconate titanate film were then investigated by means of the AFM method. Asvestas et al [8] defined a modified version to estimate the Fractal Dimension of two variable Fractional Brownian Motion functions from its average power spectrum. The method is called the Power Differentiation method.…”

Section: Introductionmentioning

confidence: 99%

Multiresponse Optimization of Edm Process with Nanofluids Using Topsis Method and Genetic Algorithm

Prabhu¹,

Vinayagam²

2016

Archive of Mechanical Engineering

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“…Par ailleurs, Asvestas et al [6] ont montré que cette méthode n'est pas stable numériquement. En effet, après l'avoir testé sur un ensemble d'images fractales générées par la méthode du déplacement aléatoire du point médian, ils ont souligné le fait que la méthode sous-estimait la valeur théorique de la DF.…”

Section: Méthode De « Comptage Différentiel Des Boîtes » (Differentiaunclassified

La géométrie fractale pour l’analyse de signaux médicaux : état de l’art

Lopes

Dubois

Bhouri

et al. 2010

IRBM

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“…The theory of self-similarity should be defined as the object is precisely or something like related to a part of itself; alternatively we can say that if a surrounded set A is supposed to be self-similar, if A is the unification of a number (Nr) of non-overlapping scaled copies of itself, where r is the reduction factor reported in [1]. Fractal geometry also gives a mathematical special model of various difficult objects initiate in nature [1][2][3], that includes coastline, mountains, and clouds and also it has been useful in different texture analysis such as segmentation [4][5][6], shape measurement and classification [7], image and graphic analysis in different fields [8,9]. In this regard, different researchers are contributed their work, such as Gangepain and Roques-carmes presented reticular cell counting method [10,11] and later on Keller et al proposed probability box counting [10,12].…”

Section: Introductionmentioning

confidence: 99%

On Calculation of Fractal Dimension of Color Images

Nayak¹,

Mishra²

2017

IJIGSP

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Abstract-Fractal Dimension is a basic parameter of fractal geometry and it has been applied in many fields of application including image analysis, texture segmentation, and shape classification. Many fractal dimensions methods have been evolved depending upon different types of images that could be differentiated with greater precision. In this paper, we propose a color approach based on the modified differential box-counting method to estimate fractal dimension of color images in terms of its smoothness. Here we have experimented on four sets of color images like; sixteen number of real natural texture images, eight sets of controlled experimental fabric images with varied color and texture, twelve numbers of generated synthetic images and four smoothed images of known fractal dimension. The results demonstrated that the said proposed method shows accurate fractal dimension estimation of color texture image and also it indicates FD as 2 for smoothed images, which has already been developed in last decade and indicates higher roughness in color images, to check the accuracy of our proposed method, we used a set of twelve synthetic generated images.

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A Power Differentiation Method of Fractal Dimension Estimation for 2-D Signals

Cited by 40 publications

References 21 publications

Multiresponse Optimization of Edm Process with Nanofluids Using Topsis Method and Genetic Algorithm

Multiresponse Optimization of Edm Process with Nanofluids Using Topsis Method and Genetic Algorithm

La géométrie fractale pour l’analyse de signaux médicaux : état de l’art

On Calculation of Fractal Dimension of Color Images

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